Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24918401 | C2 | semidirect |
| 3. #24908441 | C2 | semidirect |
| 4. #24906131 | C2 | semidirect |
| 5. #24906130 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 7. C83×#3208 | C2 | semidirect |
| 48. C4⋊(C83⋊C8) | D4 | semidirect |
| 56. C4⋊Q8×C83 | D4 | semidirect |
| 57. C4⋊Q8×C83 | D4 | semidirect |
| 69. C4⋊C8×C83 | D4 | semidirect |
| 95. C4×Dic83 | SD16 | semidirect |
| 200. #3208 | D83 | semidirect |
| 206. C83 | #10290 | semidirect |
| 238. C4⋊Q8 | C22⋊D83 | semidirect |
| 239. C4⋊Q8 | C22⋊D83 | semidirect |
| 265. C4⋊C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918401 | 2 |
| #24915857 | 2 |
| #24908441 | 2 |
| #24906131 | 2 |
| #24906130 | 2 |
| #24905295 | 2 |
| C83×#3208 | 2 |
| #10290 | 83 |